In a conventional water-cooled generator for motor vehicles, for example as described in French Patent Application No. 2 717 638, the stator and rotor are accommodated in a pot-shaped housing which, on one hand, is inserted into a pot-shaped encasing in such a manner that an annular space remains between the covering of the pot-shaped encasing and the outer surface of the housing, the annular space being covered in a fluid-tight manner on one side by the bottom of the encasing, and on the other side, by a cover mounted on the pot edge of the encasing and housing. The annular space, on sides turned away from each other, includes an inflow orifice and a discharge orifice which are each enclosed by a connecting piece, projecting radially on the encasing, for a water pipe. The water circulated by a pump in a circulation circuit enters into the annular space through the inflow orifice, circumflows the housing, and exits the annular space again via the discharge orifice. The heat emitted by the generator is absorbed by the cooler water and carried away.